In the denominator of one fraction, you have "\(\displaystyle \frac{2}{3}\)" when you clearly mean "\(\displaystyle 3^2\)". Also, the Laplace transform of \(\displaystyle e^{3t}cosh(3t)\) is \(\displaystyle \frac{s- 3}{(s- 3)^2+ 3^2}\).
You would be better advised to separate your fraction as \(\displaystyle \frac{2s- 1}{(s- 3)^2- 3^2}= 2\frac{s- 3}{(s- 3)^2- 3^2}+ 4\frac{1}{(s- 3)^2- 3^2}\)
